Related papers: The Local Action Lemma

We give new algorithms based on Markov chains to sample and approximately count satisfying assignments to $k$-uniform CNF formulas where each variable appears at most $d$ times. For any $k$ and $d$ satisfying $kd<n^{o(1)}$ and $k\ge 20\log…

Fine-tuning large language models (LLMs) with low-rank adaptations (LoRAs) has become common practice, often yielding numerous copies of the same LLM differing only in their LoRA updates. This paradigm presents challenges for systems that…

The local convergence of alternating optimization methods with overrelaxation for low-rank matrix and tensor problems is established. The analysis is based on the linearization of the method which takes the form of an SOR iteration for a…

In this paper, we establish a local limit theorem for linear fields of random variables constructed from independent and identically distributed innovations each with finite second moment. When the coefficients are absolutely summable we do…

In this note, we show that the Local Molecular Field theory of Weeks et. al. can be re-derived as an extremum problem for an approximate Helmholtz free energy. Using the resulting free energy as a classical, fluid density functional yields…

This paper proposes a local representation for Empirical Likelihood (EL). EL admits the classical local linear quadratic representation by its likelihood ratio property. A local estimator is derived by using the new representation.…

We have recently witnessed that ``Intelligence" and `` Compression" are the two sides of the same coin, where the language large model (LLM) with unprecedented intelligence is a general-purpose lossless compressor for various data…

The local pivotal method (LPM) is a successful sampling method for taking well-spread samples from discrete populations. We show how the LPM can be utilized to sample from arbitrary continuous distributions and thereby give powerful…

Local Search is one of the fundamental approaches to combinatorial optimization and it is used throughout AI. Several local search algorithms are based on searching the k-exchange neighborhood. This is the set of solutions that can be…

Many randomized algorithms can be derandomized efficiently using either the method of conditional expectations or probability spaces with low (almost-) independence. A series of papers, beginning with Luby (1993) and continuing with Berger…

Locality-sensitive hashing (LSH) is a fundamental technique for similarity search and similarity estimation in high-dimensional spaces. The basic idea is that similar objects should produce hash collisions with probability significantly…

We introduce a group of related methods for binary classification tasks using probes of the hidden state activations in large language models (LLMs). Performance is on par with the largest and most advanced LLMs currently available, but…

The material presented in this paper contributes to establishing a basis deemed essential for substantial progress in Automated Deduction. It identifies and studies global features in selected problems and their proofs which offer the…

Tool-using agents based on Large Language Models (LLMs) excel in tasks such as mathematical reasoning and multi-hop question answering. However, in long trajectories, agents often trigger excessive and low-quality tool calls, increasing…

Local Linear embedding (LLE) is a popular dimension reduction method. In this paper, we first show LLE with nonnegative constraint is equivalent to the widely used Laplacian embedding. We further propose to iterate the two steps in LLE…

Automating formal proofs of combinatorial identities is challenging for LLM-based provers, as long-horizon proof planning is required and unconstrained search quickly explodes. Symbolic methods such as the Wilf-Zeilberger (WZ) method can…

Large Neighborhood Search (LNS) is a common heuristic in combinatorial optimization that iteratively searches over a large neighborhood of the current solution for a better one. Recently, neural network-based LNS solvers have achieved great…

We give a model of how to infer natural language rules by doing experiments. The model integrates Large Language Models (LLMs) with Monte Carlo algorithms for probabilistic inference, interleaving online belief updates with experiment…

Applying local search algorithms to combinatorial optimization problems is not an easy feat. Typically, human intervention is required to compile the constraints to input data for some metaheuristic algorithm. In this paper, we establish a…

Typing of lambda-terms in Elementary and Light Affine Logic (EAL, LAL, resp.) has been studied for two different reasons: on the one hand the evaluation of typed terms using LAL (EAL, resp.) proof-nets admits a guaranteed polynomial…